I might be a little out of date, and not understanding the problem correctly, but if you're referring to the chuck coming loose from the arbor in most cases the taper on the drill chuck is a Jacobs taper, not a Morse taper. The Morse taper is usually the taper where the arbor fits into the spindle.
You can buy either Jacobs or Morse taper reamers, however in most cases they're more expensive than a new arbor. There are several #3 Morse taper reamers (arbor to spindle) listed on eBay for between $15.00 and $50.00. There are also a number of #3 Jacobs taper reamers available from online industrial supply vendors. These however are generally in the $75.00 and higher range.
I would suggest contacting a few commercial machine shops in your area. If they have either style I think they would be able to ream and fit the chuck (or arbor) for far less money than it would cost to purchase a tool that would likely be used only once.